The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A356817 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A356817

a(n) = Sum_{k=0..n} (-1)^k * (k*n-1)^(n-k) * binomial(n,k).
(history; published version)

#11 by Michael De Vlieger at Mon Aug 29 16:36:01 EDT 2022

STATUS

proposed

approved

#10 by Seiichi Manyama at Mon Aug 29 13:06:39 EDT 2022

STATUS

editing

proposed

#9 by Seiichi Manyama at Mon Aug 29 10:52:36 EDT 2022

FORMULA

a(n) = [x^n] Sum_{k>=0} (-x)^k / (1 - (n*k-1)*x)^(k+1).

#8 by Seiichi Manyama at Mon Aug 29 10:08:00 EDT 2022

FORMULA

a(n) = n! * [x^n] exp( -x * (exp(n * x) + 1) ).

#7 by Seiichi Manyama at Mon Aug 29 10:06:54 EDT 2022

DATA

1, -2, 0, 1, 144, 4143, 110368, 2535475, 13299968, -5169863825, -639341093376, -59073970497885, -4677854594527232, -276406098219258425, 2399871442122924032, 5163244810691492730907, 1331213942683118587674624, 262517264591996332314037215

#6 by Seiichi Manyama at Mon Aug 29 10:00:13 EDT 2022

CROSSREFS

Cf. A356815, A356816, A356818.

#5 by Seiichi Manyama at Mon Aug 29 09:55:31 EDT 2022

CROSSREFS

Cf. A356806, A356811, A356814.

#4 by Seiichi Manyama at Mon Aug 29 09:54:37 EDT 2022

PROG

(PARI) a(n) = sum(k=0, n, (-1)^k*(k*n-1)^(n-k)*binomial(n, k));

#3 by Seiichi Manyama at Mon Aug 29 09:53:43 EDT 2022

NAME

a(n) = Sum_{k=0..n} (-1)^k * (k*n-1)^(n-k) * binomial(n,k).~

#2 by Seiichi Manyama at Mon Aug 29 09:53:06 EDT 2022

NAME

allocated for Seiichi Manyama

a(n) = Sum_{k=0..n} (-1)^k * (k*n-1)^(n-k) * binomial(n,k).~

DATA

1, -2, 0, 1, 144, 4143, 110368, 2535475, 13299968, -5169863825, -639341093376, -59073970497885, -4677854594527232, -276406098219258425

OFFSET

0,2

KEYWORD

allocated

sign

AUTHOR

Seiichi Manyama, Aug 29 2022

STATUS

approved

editing